Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af3m)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.af3m.01

Input Form

HypergeometricPFQ[{17/4}, {-(7/2), -(13/4)}, z] == (1/(35933625 Sqrt[2])) (z^(1/4) ((35933625 + 85293000 z + 76237200 z^2 + 43056000 z^3 + 125798400 z^4 + 86016000 z^5 + 524288 z^6) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-35933625 - 56546100 z - 33555600 z^2 - 19918080 z^3 + 101928960 z^4 + 5832704 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (35933625 + 27799200 z + 13871520 z^2 + 10483200 z^3 + 20078592 z^4 + 131072 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]